John S. Villarrubia

Algorithms for Scanned Probe Microscope Image Simulation, Surface Reconstruction , and Tip Estimation

To the extent that tips are not perfectly sharp, images produced by scanned probe microscopies (SPM) such as atomic force microscopy and scanning tunneling microscopy are only approximations of the specimen surface. Tip-induced distortions are significant whenever the specimen contains features with aspect ratios comparable to the tip’s. Treatment of the tip-surface interaction as a simple geometrical exclusion allows calculation of many quantities important for SPM dimensional metrology. Algorithms for many of these are provided here, including the following: (1) calculating an image given a specimen and a tip (dilation), (2) reconstructing the specimen surface given its image and the tip (erosion), (3) reconstructing the tip shape from the image of a known “tip characterizer” (erosion again), and (4) estimating the tip shape from an image of an unknown tip characterizer (blind reconstruction). Blind reconstruction, previously demonstrated only for simulated noiseless images, is here extended to images with noise or other experimental artifacts. The main body of the paper serves as a programmer’s and user’s guide. It includes theoretical background for all of the algorithms, detailed discussion of some algorithmic problems of interest to programmers, and practical recommendations for users.

Nanoindentation of polymers : An overview

In this paper, the application of instrumented indentation devices to the measurement of the elastic modulus of polymeric materials is reviewed. This review includes a summary of traditional analyses of load-penetration data and a discussion of associated uncertainties. Also, the use of scanning probe microscopes to measure the nanoscale mechanical response of polymers is discussed, particularly with regard to the associated limitations. The application of these methods to polymers often leads to measurements of elastic modulus that are somewhat high relative to bulk measurements with potentially artificial trends in modulus as a function of penetration depth. Also, power law fits to indentation unloading curves are often a poor representation of the actual data, and the power law exponents tend to fall outside the theoretical range. These problems are likely caused by viscoelasticity, the effects of which have only been studied recently. Advancement of nanoindentation testing toward quantitative characterization of polymer properties will require materialindependent calibration procedures, polymer reference materials, advances in instrumentation, and new testing and analysis procedures that account for viscoelastic and viscoplastic polymer behavior.

Morphological estimation of tip geometry for scanned probe microscopy

Abstract Morphological constraints inherent in the imaging process limit the possible shapes of the tip with which any given tunneling microscope or atomic force microscope image could have been taken. Broad tips do not produce narrow image protrusions. Therefore, feature sizes within the image may be used to place an upper bound on the size of the tip. In this paper, mathematical morphology is used to derive, for each point on an image, a corresponding bounding surface for the tip. The actual tip must be equal to or smaller than the largest tip which satisfies all of the constraints. Example calculations are performed, demonstrating that if the imaged specimen contains sharp features and high relief, the tip shape deduced by this method will be a good estimate of the actual one. Once known, the tip geometry can be “deconvoluted” from images to recover parts of the actual surface which were accessible to the tip.

Experimental test of blind tip reconstruction for scanning probe microscopy

Determination of the tip geometry is a prerequisite to converting the scanning probe microscope (SPM) from a simple imaging instrument to a tool that can perform width measurements accurately. Recently we developed blind reconstruction, a method to characterize the SPM tip shape. In principle this method allows estimation of the tip shape from an image of a tip characterizer sample that need not be known independently. In this work, we compare blind reconstruction results to those obtained by scanning electron microscopy for two diamond stylus profiler tips, one of which has a gentle shape and the other a more complicated profile. Of the two comparisons, the poorer agreement is still better than 30 nm for parts of the tip within a several micrometer neighborhood of the apex. In both cases the differences are comparable to the combined standard uncertainties of the measurements. We estimate uncertainties from five sources, the most significant of which is the repeatability of the stylus profiling instrument. In a separate measurement we determine the geometry of a silicon nitride SPM tip. The measured radius, 4-fold symmetry, included angle, and tilt are all consistent with expectations for such a tip.

Scanned probe microscope tip characterization without calibrated tip characterizers

In scanned probe microscopy the image is a combination of information from the sample and the tip. In order to reconstruct the true surface geometry, it is necessary to know the actual tip shape. It has been proposed that this shape may be reconstructed from images of ‘‘tip characterizer’’ artifacts of independently known shape. The requirements for this strategy—dimensional uncertainty and instability of the characterizer small compared to the tip size—are not trivial. An alternative is ‘‘blind reconstruction,’’ which requires no information about the characterizer geometry apart from that contained within its image, yet produces an outer bound on the tip shape which for appropriately chosen characterizers is a good approximation. With blind reconstruction dimensional instability of characterizers is less problematical, and characterizer measurability is no longer a constraint, so more complex distributed characterizer geometries may be advantageously employed. In situations where part of a characterizer...

Determination of optimal parameters for CD-SEM measurement of line-edge roughness

The measurement of line-edge roughness (LER) has recently become a topic of concern in the litho-metrology community and the semiconductor industry as a whole. The Advanced Metrology Advisory Group (AMAG), a council composed of the chief metrologists from the International SEMATECH (ISMT) consortium’s Member Companies and from the National Institute of Standards and Technology (NIST), has a project to investigate LER metrics and to direct the critical dimension scanning electron microscope (CD-SEM) supplier community towards a semiconductor industry-backed, standardized solution for implementation. The 2003 International Technology Roadmap for Semiconductors (ITRS) has included a new definition for roughness. The ITRS envisions root mean square measurements of edge and width roughness. There are other possible metrics, some of which are surveyed here. The ITRS envisions the root mean square measurements restricted to roughness wavelengths falling within a specified process-relevant range and with measurement repeatability better than a specified tolerance. This study addresses the measurement choices required to meet those specifications. An expression for the length of line that must be measured and the spacing of measurement positions along that length is derived. Noise in the image is shown to produce roughness measurement errors that have both random and nonrandom (i.e., bias) components. Measurements are reported on both UV resist and polycrystalline silicon in special test patterns with roughness typical for those materials. These measurements indicate that the sensitivity of a roughness measurement to noise depends importantly both on the choice of edge detection algorithm and the quality of the focus. Measurements are less sensitive to noise when a model-based or sigmoidal fit algorithm is used and when the images are in good focus. Using the measured roughness characteristics for UV resist lines and applying the ITRS requirements for the 90 nm technology node, the derived expression for sampling length and sampling interval implies that a length at least 8 times the node (i.e., 720 nm) must be measured at intervals of 7.5 nm or less.

Scanning electron microscope analog of scatterometry

Optical scatterometry has attracted a great deal of interest for linewidth measurement due to its high repeatability and capability of measuring sidewall shape. We have developed an analogous and complementary technique for the scanning electron microscope. The new method, like scatterometry, measures shape parameters (e.g., wall angles) as well as feature widths. Also like scatterometry, it operates by finding a match between the measured signal from an unknown sample and a library of signals calculated for known samples. A physics-based model of the measurement is employed for the calculation of libraries. The method differs from scatterometry in that the signal is an image rather than a scattering pattern, and the probe particles are electrons rather than photons. Because the electron-sample interaction is more highly localized, isolated structures or individual structures within an array can be measured. Results of this technique were compared to an SEM cross section for an isolated polycrystalline silicon line. The agreement was better than 2 nm for the width and 0.2{degrees} for wall angles, differences that can be accounted for by measurement errors arising from line edge roughness.

Blind estimation of general tip shape in AFM imaging

The use of flared tip and bi-directional servo control in some recent atomic force microscopes (AFM) has made it possible for these advanced AFMs to image structures of general shapes with undercut surfaces. AFM images are distorted representations of sample surfaces due to the dilation produced by the finite size of the tip. It is necessary to obtain the tip shape in order to correct such tip distortion. This paper presents a noise-tolerant approach that can for the first time estimate a general 3-dimensional (3D) tip shape from its scanned image in such AFMs. It extends an existing blind tip estimation method. With the samples, images, and tips described by dexels, a representation that can describe general 3D shapes, the new approach can estimate general tip shapes, including reentrant features such as undercut lines.

Dimensional metrology of resist lines using a SEM model-based library approach

The widths of 284 lines in a 193 nm resist were measured by two methods and the results compared. One method was scanning electron microscopy (SEM) of cross-sections. The other was a model-based library (MBL) approach in which top-down CD-SEM line scans of structures are compared to a library of simulated line scans, each one of which corresponds to a well-defined sample structure. Feature edge shapes and locations are determined by matching measured to simulated images. This way of determining critical dimensions makes use of known physics of the interaction of the electron beam with the sample, thereby removing some of the ambiguity in sample edge positions that are assigned by more arbitrary methods. Thus far, MBL has shown promise on polycrystalline silicon samples [Villarrubia et al., Proc. SPIE 4689, pp. 304-312 (2002)]. Resist lines, though important in semiconductor manufacturing, pose a more difficult problem because resist tends to shrink and charge upon electron beam exposure. These phenomena are not well characterized, and hence are difficult to include in the models used to construct libraries. Differences between the techniques had a systematic component of 3.5 nm and a random component of about 5 nm. These differences are an upper bound on measurement errors attributable to resist properties, since they are partly attributable to other causes (e.g,. linewidth roughness).

Monte Carlo modeling of secondary electron imaging in three dimensions

Measurements of critical dimensions (CDs), roughness, and other dimensional aspects of semiconductor electronics products rely upon secondary electron (SE) images in the scanning electron microscope (SEM). These images are subject to artifacts at the nanometer size scale that is relevant for many of these measurements. The most accurate measurements for this reason depend upon models of the probe-sample interaction in order to perform corrections. MONSEL, a Monte Carlo simulator intended primarily for CD metrology, has been providing the necessary modeling. However, restrictions on the permitted sample shapes are increasingly constraining as the industrys measurement needs evolve towards inherently 3-dimensional structures. We report here results of a collaborative project, in which the MONSEL physics has been combined with the 3D capabilities of NISTMonte, another NIST Monte Carlo simulator that was previously used principally to model higher energy electrons and x-rays. Results from the new simulator agree very closely with the original MONSEL for samples within the repertoire of both codes. The new codes predicted SE yield variation with angle of incidence agrees well with preexisting measurements for light, medium, and heavy elements. Capabilities of the new code are demonstrated on a model of a FinFET transistor.